Question

Evaluate ∫ (4 sin x – 3 cos x) dx.

Answer 1

Answer:

-4cosx - 3sinx

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Answer 2

Given:

A mathematical integration ∫ (4sinx – 3cosx)dx.

To Find:

The integral of the above function.

Solution:

The given problem can be solved using the concepts of integration.

1. The given integral is ∫ (4sinx – 3cosx)dx.

2. According to the concepts of integration,

• ∫sinx dx = -cosx + c,

• ∫cosx dx = sinx + c,

3. Use the above formula in the given questions,

=> ∫ (4sinx – 3cosx)dx = ∫(4sinx)dx – ∫(3cosx)dx,

=> ∫ (4 sin x – 3 cos x) dx = 4∫(sinx)dx – 3∫(cosx)dx,

=> ∫(4sinx)dx – ∫(3cosx)dx = 4(-cosx) - 3(sinx) +c,

=> ∫ (4 sin x – 3 cos x) dx. = -4cosx -3sinx + c.

Therefore, the value of ∫ (4sinx – 3 cos x)dx is -4cosx -3sinx + c.